When people address early mathematics education, commonly they write or reference policies, standards, "scope and sequences" and curriculum, or documents on instructional strategies. These are important; however, we believe that the core consideration should be the nature of mathematics and the development of mathematics "in children." An 80-year-old incident illustrates what we mean. A mother attending parents' night asked Fawcett (1938), "How is Willie doing in mathematics?" Fawcett replied: "Madam, you ask the wrong question. You should ask, 'How is mathematics doing in Willie?'" This is what we mean by the "nature of mathematics and the development of mathematics in children": The mathematics that "does well in Willie" and all other children. We develop this position by describing "learning trajectories" and our theoretical framework for them, "Hierarchic Interactionalism." [For the complete proceedings, see ED606531.]